We discuss the proportionally fair allocation of a set of indivisible items to k agents. We assume that each agent specifies only a ranking of the items from best to worst. Agents do not specify their valuations of the items. An allocation is proportionally fair if all agents believe that they have received their fair share of the value according to how they value the items.
We give simple conditions (and a fast algorithm) for determining whether the agents rankings give sufficient information to determine a proportionally fair allocation. An important special case is a divorce situation with two agents. For such a divorce situation, we provide a particularly simple allocation rule that should have applications in the real world.
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